For over two decades, Professor Liu has led his team in exploring the patterns and laws of language systems through approaches such as dependency grammar, valency theory, quantitative linguistics, and complex networks. Their work has resulted in a series of internationally influential scientific achievements. Below are some of their major scientific discoveries, theoretical contributions, and perspectives.

Probabilistic Valency Pattern (PVP) is a theoretical framework in natural language processing. Compared to existing theoretical models, the PVP framework not only better describes the actual structure of language and explains certain behaviors observed in statistical language (syntactic) parsers but also contributes to a more psychologically realistic interpretation and simulation of human language processing mechanisms.

Liu-Directionalities, a research method for linguistic typology based on dependency treebanks, reveals that word order typology is continuous rather than discrete. The method introduced and validated a way to derive dependency direction for studying word order typology directly from corpora. This approach to linguistic typology, grounded in annotated real-world corpora, has been referred to by international scholars as ‘Liu-Directionalities’, representing a new probabilistic method for exploring syntactic parameters and a novel, advanced approach to modern linguistic typology.

Dependency Distance Minimization (DDM) is a human tendency to manage cognitive load in (dependency) syntactic relationships. Empirical data from 20 languages validated three related hypotheses: 1) the human language processing mechanism favors word orders that minimize the mean dependency distance (MDD) of sentences; 2) there exists a threshold for MDD in human languages; and 3) the collaboration between grammar and cognition ensures that the dependency distances in languages remain within this threshold.

Language Complex Networks, such as syntactic complex networks, are powerful tools for studying the systematic characteristics of language. Syntax influences language networks to some extent, but when determining whether a network is a syntactic network, being scale-free is a necessary condition, not a sufficient one. Key parameters of syntactic complex networks can serve as indicators for language classification. Using complex network methods, it has been found that, unlike first-language acquisition, syntactic emergence does not occur during second-language learning.

Language is a human-driven complex adaptive system. Language is a symbol system shaped and driven by humans. Therefore, language studies should take into account, as much as possible, the role and constraints of human cognitive abilities in the formation and evolution of linguistic structural patterns. Language is also a complex adaptive system, which necessitates that research go beyond examining its individual elements. Instead, it should focus on the collaborative relationships among its various elements.

Quantitative linguistics methods help uncover patterns from linguistic data and elevate them to linguistic laws. For example: the probability distributions of most dependency relations conform to the Zipf-Alekseev distribution; the senses of English verbs follow a positive-negative binomial distribution; the complementation patterns of English verbs and adjectives follow a power-law distribution, whereas those of nouns conform to the Zipf-Mandelbrot distribution; the frequency-rank distribution of valency and polysemy in Chinese conforms to a power law; the dependency distance distribution of short sentences generally follows an exponential distribution, while longer sentences tend to follow a power-law distribution; the occurrence frequencies of words at various hierarchical levels in human language sentences conform to distribution patterns.